Rabi N. Bhattacharya

1. Front Matter

   Pages i-xxi

   PDF

2. Modes of Approximation

   1. Front Matter

      Pages 1-1

      PDF

   2. Contributions of Rabi Bhattacharya to the Central Limit Theory and Normal Approximation

      • Peter Hall

      Pages 3-13

   3. Asymptotic Expansions for Stochastic Processes

      • Nakahiro Yoshida

      Pages 15-32

   4. An Introduction to Normal Approximation

      • Qi-Man Shao

      Pages 33-40

   5. Reprints: Part I

      • R. N. Bhattacharya

      Pages 41-127

3. Large Time Asymptotics for Markov Processes I: Diffusion

   1. Front Matter

      Pages 129-129

      PDF

   2. Martingale Methods for the Central Limit Theorem

      • S. R. Srinisava Varadhan

      Pages 131-135

   3. Ergodicity and Central Limit Theorems for Markov Processes

      • Thomas G. Kurtz

      Pages 137-154

   4. Reprints: Part II

      • R. N. Bhattacharya

      Pages 155-262

4. Large Time Asymptotics for Markov Processes II: Dynamical Systems and Iterated Maps

   1. Front Matter

      Pages 263-263

      PDF

   2. Dynamical Systems, IID Random Iterations, and Markov Chains

      • Krishna B. Athreya

      Pages 265-275

   3. Random Dynamical Systems and Selected Works of Rabi Bhattacharya

      • Edward C. Waymire

      Pages 277-288

   4. Reprints: Part III

      • R. N. Bhattacharya

      Pages 289-359

5. Stochastic Foundations in Applied Sciences I: Economics

   1. Front Matter

      Pages 361-361

      PDF

   2. Stability Analysis for Random Dynamical Systems in Economics

      • Takashi Kamihigashi, John Stachurski

      Pages 363-374

   3. Some Economic Applications of Recent Advances in Random Dynamical Systems

      • Santanu Roy

      Pages 375-383

   4. Reprints: Part IV

      • R. N. Bhattacharya

      Pages 385-407

6. Stochastic Foundations in Applied Sciences II: Geophysics

   1. Front Matter

      Pages 409-409

      PDF

   2. Advection-Dispersion in Fluid Media and Selected Works of Rabi Bhattacharya

      • Enrique A. Thomann, Edward C. Waymire

      Pages 411-423

This volume presents some of the most influential papers published by Rabi N. Bhattacharya, along with commentaries from international experts, demonstrating his knowledge, insight, and influence in the field of probability and its applications.  For more than three decades, Bhattacharya has made significant contributions in areas ranging from theoretical statistics via analytical probability theory, Markov processes, and random dynamics to applied topics in statistics, economics, and geophysics.  Selected reprints of Bhattacharya’s papers are divided into three sections: Modes of Approximation, Large Times for Markov Processes, and Stochastic Foundations in Applied Sciences.  The accompanying articles by the contributing authors not only help to position his work in the context of other achievements, but also provide a unique assessment of the state of their individual fields, both historically and for the next generation of researchers.


Rabi N. Bhattacharya: Selected Papers will be a valuable resource for young researchers entering the diverse areas of study to which Bhattacharya has contributed.  Established researchers will also appreciate this work as an account of both past and present developments and challenges for the future.

• Rabi N. Bhattacharya
• Markov processes
• Probability Approximation
• Random Dynamical Systems
• Stochastic Foundations
• Diffusion

“The volume offers analytic probability theory, statistic theory, Markov processes, random dynamic systems, and applied topics in statistics, economics and geophysics … . This volume can be very useful for researchers in probability and statistics, as well as those practitioners in economics, geophysics and statistics. … The other target audience consists of theoretic probability PhD students and researchers, stochastic processes and random dynamics researchers and applied practicers … .” (Weiping Li, zbMATH 1378.60010, 2018)



“I enjoyed rereading some of the articles with interest and pleasure. This collection has some nice collection of statistical and related works and provides some historical perspectives of some of the important work in respective scientific fields produced by Bhattacharya. Surely, this volume will be of interest to researchers in probability and statistics with applications in diverse fields. Certainly, this volume is a one-stop shopping and contains wealth of information.” (S. Ejaz Ahmed, Technometrics, Vol. 59 (4), November, 2017)

• Mathematics, The Pennsylvania State University, State College, USA

  Manfred Denker

• Department of Mathematics, Oregon State University, Corvallis, USA

  Edward C. Waymire

Policies and ethics